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Newton's method for symmetric quartic polynomials

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We investigate the parameter plane of the Newton's method applied to the family of quartic polynomials $p_{a,b}(z)=z^4+az^3+bz^2+az+1$, where $a$ and $b$ are real parameters. We divide the parameter plane $(a,b) \in \mathbb R^2$ into twelve open and connected {\it regions} where $p$, $p'$ and $p''$ have simple roots. In each of these regions we focus on the study of the Newton's operator acting on the Riemann sphere.

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Applied Mathematics and Computation, 2016, vol. 290, p. 326-335

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Articles publicats en revistes (Matemàtiques i Informàtica)

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Newton's method for symmetric quartic polynomials